CN102547694A - Chinese-remainder-theorem-based group key creation method for sensor network - Google Patents

Chinese-remainder-theorem-based group key creation method for sensor network Download PDF

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CN102547694A
CN102547694A CN2012100373224A CN201210037322A CN102547694A CN 102547694 A CN102547694 A CN 102547694A CN 2012100373224 A CN2012100373224 A CN 2012100373224A CN 201210037322 A CN201210037322 A CN 201210037322A CN 102547694 A CN102547694 A CN 102547694A
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node
key
group key
calculate
secret
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温蜜
雷景生
杨俊杰
叶文珺
陈克非
孙超超
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Shanghai University of Electric Power
University of Shanghai for Science and Technology
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Shanghai University of Electric Power
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Abstract

The invention relates to a Chinese-remainder-theorem-based group key creation method for a sensor network. A pre-distribution way is adopted, and secrete information is preset before sensor nodes are distributed in a specific area, and is used for computing a group key; and the group key can be updated under the condition of addition of a new node or deletion of an old node, so that the security of the network is ensured. In addition, compared with an ordinary symmetric-mechanism-based key management scheme, the method has higher anti-attack capability and cryptanalysis capability. A public-key-property-based key management mechanism for the sensor network is favorable for an upper-layer network such as transmission-layer and application-layer networks in the Internet of things to expand and use a public key algorithm.

Description

In a kind of sensor network based on the group key method for building up of Chinese remainder theorem
Technical field
The present invention relates to a kind of sensor network security technology, in particularly a kind of sensor network based on the group key method for building up of Chinese remainder theorem.
Background technology
In wireless sensor network, in order to ensure information security, internodal communication often need be adopted safety measure protection.In all security mechanisms, encryption technology is the basis, can realize demands for security such as sensor network authentication, confidentiality, non-repudiation, integrality through encrypting.For encryption technology, encrypt and mainly contain two chief components, i.e. algorithm and key.Through years of researches and development, AES has had very ripe international standard, such as: DES, AES etc., we can select based on the concrete application of sensor network.But no matter how powerful cryptographic algorithm is, we need first arranging key when carrying out confidential corespondence, if the key generation method a little less than having used, whole system all is weak and do not spent the decoding AES so.Therefore the prerequisite that is a robust system with a strong key schedule, key management that Here it is.Therefore the key management in the sensor network becomes the key factor that influences network security.
According to tracking and the analysis to the domestic and international research document, in recent years, scholars both domestic and external had proposed multiple IKMP to wireless sensor network.Yet most of agreements are paid close attention to all is the performance of the aspects such as connectedness, survivability, validity to key.After sensor network is linked into Internet of Things as sensing layer, the safety of information will receive the attack and the interference at all kinds terminal in the network.Want the safety of guarantee information, the key in the sensor network will more need improve its anti-attack ability or autgmentability.
Existing key managing project, they all concentrate on based on the key management of symmetric property and research.Though these key managing projects also can play secret effect to a certain extent.But its anti-attack ability also is not very strong; And in a single day be extended in the Internet of Things, its part based on the symmetric key management possibly become the weakness of whole network attack.
Summary of the invention
The present invention be directed to the weak problem of key management anti-attack ability of wireless sensor network communication node; Having proposed in a kind of sensor network based on the group key method for building up of Chinese remainder theorem, is that a kind of combination secret sharing and Chinese remainder theorem make up the group key management scheme.Its anti-attack and cryptanalytic ability strengthen to some extent, and the method helps expansion and the use of its upper layer network (like the transport layer in the Internet of Things, the application layer network) to the public-key cryptographic keys algorithm based on the sensor network cipher key administrative mechanism of PKI character.
Technical scheme of the present invention is: based on the group key method for building up of Chinese remainder theorem, the method concrete steps are following in a kind of sensor network:
1) supposes to exist in the network base-station node BS and n general node, Gc=(N 1, N 2. .., N n) be the initial sets of n general node;
2) process of the generation of secret information and node initializing is:
The first step: BS selects n coprime in twos integer q 1, q 2..., q n, let them as the private information of n node,, work as i here During j Gcd (q i , q j )=1BS selects a polynomial f (x)=a at random then 1X+a 0, make K gBe group key, and with it as once polynomial constant term, i.e. a 0=K gBS produces the input of two integers as f (x) at random, obtains two secret sharing S 0And S g, S gBe to be used for the shield group key K g;
Second step: BS uses S gAnd q i(i=1 ..., n) produce n following son secret:
Figure 2012100373224100002DEST_PATH_IMAGE002
BS is again by P=q 1q 2... q n, P i=P/q i(i=1 ..., n) calculate PWith P i
It also will be by P simultaneously iP i'=1 mod q iCalculate P i' (i=1 ..., n);
Further BS calculates y again i=c iP iP i' and s i=y iP;
The 3rd step: BS is with message { s 1..., s n, P 1..., P n, S 0Be broadcast to nodes all in the network, if between BS and each node pair key is arranged, it also can use each node N iKey is carried out secret transmission to broadcast, as:
Figure 66331DEST_PATH_IMAGE003
3) recovery process of group key:
After each node receives the message that base station BS sends, node N iTo use the private information q of own node earlier iCalculate P=P iq i
Again according to y i=s i/ P recovers y i
Then by
Figure 2012100373224100002DEST_PATH_IMAGE004
Calculate S g
Basis receives again S 0 With calculate S g , node N iTo calculate according to the secret sharing theorem of Shamir
Go out group key K g, promptly a 0 =
Figure 466088DEST_PATH_IMAGE005
, here L i (0)Be to be by what the Lagrange's interpolation theorem calculated
Number
Figure 2012100373224100002DEST_PATH_IMAGE006
;
4) adding of new node:
Add fashionablely as a new node, the base station will be from step 2) second step beginning of process produces n+1 son secret again; Calculate P, P then in the same way i, P i', y i, s i(i=1 ..., n n+1), and is broadcast to all nodes; Node is again with the mode recovering group key in the step 3) process;
5) cancelling of node:
When a node need be cancelled from network, the base station will be from step 2) second step beginning of process produces n-1 son secret again; Calculate P, P then in the same way i, P i', y i, s i(i=1 ..., n-1), and the mode of secret key encryption is sent to all nodes with node; Node is again with the mode recovering group key in the step 3) process.
Beneficial effect of the present invention is: in a kind of sensor network of the present invention based on the group key method for building up of Chinese remainder theorem; That adopts presorts the mode of sending out; Before sensor node is spread in concrete zone, just preset secret information, utilized secret information calculated group group key then; Also can the update group key under the situation that new node adds or old node is cancelled, this has guaranteed the fail safe of network.In addition, its anti-attack and cryptanalytic ability force rate generally are eager to excel based on the key managing project of symmetry mechanism.Sensor network cipher key administrative mechanism based on PKI character helps expansion and the use of its upper layer network (like the transport layer in the Internet of Things, the application layer network) to the public-key cryptographic keys algorithm.
Embodiment
Chinese remainder theorem: if supposition q 1 ..., q m Be mCoprime in twos positive integer is promptly worked as i
Figure 797975DEST_PATH_IMAGE001
During j Gcd (q i , q j )=1.Suppose k 1 ..., k m Be m integer arbitrarily.Consider following congruence group:
X
Figure 2012100373224100002DEST_PATH_IMAGE008
k 1 ?mod?q 1
X
Figure 70824DEST_PATH_IMAGE008
k 2 ?mod?q 2
X
Figure 799746DEST_PATH_IMAGE008
k m ?mod?q m
Can get this equation group mould by Chinese remainder theorem MUnique solution.Here ;
Figure 2012100373224100002DEST_PATH_IMAGE010
; And can get by
Figure 501172DEST_PATH_IMAGE011
, it is exactly a unique solution.
Figure 272818DEST_PATH_IMAGE012
is inverse;
Figure 791448DEST_PATH_IMAGE014
.
For a kind of the have revocable head node of negotiation formula of self-healing ability and the cryptographic key distribution method of ordinary node are provided, the group key method for building up based on Chinese remainder theorem in a kind of sensor network of the present invention is following:
At first: in order to be without loss of generality, we suppose to exist in the network base-station node BS and n general node.Gc=(N 1, N 2. .., N n) be the initial sets of n general node, Gc=(N 1, N 2. .., N n).
1) process of the generation of secret information and node initializing is:
The first step: BS selects n coprime in twos integer q 1, q 2..., q n, let their private informations as n node.Here, work as i During j Gcd (q i , q j )=1BS selects a polynomial f (x)=a at random then 1X+a 0, make K gBe group key, and with it as once polynomial constant term, i.e. a 0=K gBS produces the input of two integers as f (x) at random, obtains two secret sharing S 0And S g, S gBe to be used for the shield group key K g.
Second step: BS uses S gAnd q i(i=1 ..., n) produce n following son secret:
Figure 24163DEST_PATH_IMAGE002
BS is again by P=q 1q 2... q n, P i=P/q i(i=1 ..., n) calculate PWith P i
It also will be by P simultaneously iP i'=1 mod q iCalculate P i' (i=1 ..., n);
Further BS calculates y again i=c iP iP i' and s i=y iP.
The 3rd step: BS is with message { s 1..., s n, P 1..., P n, S 0Be broadcast to nodes all in the network, if between BS and each node pair key is arranged, it also can use each node N iKey is carried out secret transmission to broadcast, as:
Figure 649049DEST_PATH_IMAGE003
2) recovery process of group key:
After each node receives the message that base station BS sends, node N iTo use the private information q of own node earlier iCalculate P=P iq i
Again according to y i=s i/ P recovers y i
Then by
Figure 69666DEST_PATH_IMAGE015
Calculate S g
Basis receives again S 0 With calculate S g , node N iTo calculate group key K according to the secret sharing theorem of Shamir g, promptly a 0 =
Figure 479918DEST_PATH_IMAGE005
, here L i (0)It is the coefficient that calculates by the Lagrange's interpolation theorem
3) adding of new node:
Add fashionablely as a new node, the base station will be since the 1st) second step of process produces n+1 sub-secret again; Calculate P, P then in the same way i, P i', y i, s i(i=1 ..., n n+1), and is broadcast to all nodes; Node is again with the 2nd) mode recovering group key in the process.
4) cancelling of node:
When a node need be cancelled from network, the base station will be since the 1st) second step of process produces n-1 sub-secret again; Calculate P, P then in the same way i, P i', y i, s i(i=1 ..., n-1), and the mode of secret key encryption is sent to all nodes with node; Node is again with the 2nd) mode recovering group key in the process.

Claims (1)

  1. In the sensor network based on the group key method for building up of Chinese remainder theorem, it is characterized in that the method concrete steps are following:
    1) supposes to exist in the network base-station node BS and n general node, Gc=(N 1, N 2. .., N n) be the initial sets of n general node;
    2) process of the generation of secret information and node initializing is:
    The first step: BS selects n coprime in twos integer q 1, q 2..., q n, let them as the private information of n node,, work as i here
    Figure 2012100373224100001DEST_PATH_IMAGE001
    During j Gcd (q i , q j )=1BS selects a polynomial f (x)=a at random then 1X+a 0, make K gBe group key, and with it as once polynomial constant term, i.e. a 0=K gBS produces the input of two integers as f (x) at random, obtains two secret sharing S 0And S g, S gBe to be used for the shield group key K g;
    Second step: BS uses S gAnd q i(i=1 ..., n) produce n following son secret:
    BS is again by P=q 1q 2... q n, P i=P/q i(i=1 ..., n) calculate PWith P i
    It also will be by P simultaneously iP i'=1 mod q iCalculate P i' (i=1 ..., n);
    Further BS calculates y again i=c iP iP i' and s i=y iP;
    The 3rd step: BS is with message { s 1..., s n, P 1..., P n, S 0Be broadcast to nodes all in the network, if between BS and each node pair key K is arranged In, it also can use each node N iKey is carried out secret transmission to broadcast, as:
    Figure 2012100373224100001DEST_PATH_IMAGE005
    3) recovery process of group key:
    After each node receives the message that base station BS sends, node N iTo use the private information q of own node earlier iCalculate P=P iq i
    Again according to y i=s i/ P recovers y i
    Then by
    Figure 2012100373224100001DEST_PATH_IMAGE007
    Calculate S g
    Basis receives again S 0 With calculate S g , node N iTo calculate according to the secret sharing theorem of Shamir
    Go out group key K g, promptly a 0 =
    Figure 2012100373224100001DEST_PATH_IMAGE009
    , here L i (0)Be to be by what the Lagrange's interpolation theorem calculated
    Number
    Figure 2012100373224100001DEST_PATH_IMAGE011
    ;
    4) adding of new node:
    Add fashionablely as a new node, the base station will be from step 2) second step beginning of process produces n+1 son secret again; Calculate P, P then in the same way i, P i', y i, s i(i=1 ..., n n+1), and is broadcast to all nodes; Node is again with the mode recovering group key in the step 3) process;
    5) cancelling of node:
    When a node need be cancelled from network, the base station will be from step 2) second step beginning of process produces n-1 son secret again; Calculate P, P then in the same way i, P i', y i, s i(i=1 ..., n-1), and the mode of secret key encryption is sent to all nodes with node; Node is again with the mode recovering group key in the step 3) process.
CN2012100373224A 2012-02-20 2012-02-20 Chinese-remainder-theorem-based group key creation method for sensor network Pending CN102547694A (en)

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CN102917313A (en) * 2012-10-17 2013-02-06 重庆邮电大学 Method suitable for broadcast authentication of wireless sensor network
CN104980921A (en) * 2015-06-16 2015-10-14 南京三宝科技股份有限公司 Method for key distribution in wireless sensor network
CN105072106A (en) * 2015-07-30 2015-11-18 东南大学 Identity-based Lagrange interpolation secret key management protocol
CN105657704A (en) * 2016-03-24 2016-06-08 北京理工大学 Integer modulus based wireless sensor network key management method
CN103200563B (en) * 2013-03-28 2016-06-29 重庆邮电大学 A kind of subliminal channel anonymous communication method based on authentication code
CN106507347A (en) * 2017-01-09 2017-03-15 大连理工大学 A kind of key generation method for protecting wireless sensor network security
CN108833098A (en) * 2018-07-05 2018-11-16 西北大学 A kind of key management method of wireless sensor network based on Solution for System of Linear Equations
CN109617691A (en) * 2018-11-19 2019-04-12 兰州大学 Group's authentication method and system of modular arithmetic is used in Multiuser certification
CN113726511A (en) * 2021-08-31 2021-11-30 南方电网科学研究院有限责任公司 Demand communication key distribution method and system based on Chinese remainder theorem
CN114339746A (en) * 2021-12-31 2022-04-12 中国科学技术大学 China remainder theorem-based dynamic group key management method and system for Internet of vehicles

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Cited By (17)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN102917313B (en) * 2012-10-17 2015-05-27 重庆邮电大学 Method suitable for broadcast authentication of wireless sensor network
CN102917313A (en) * 2012-10-17 2013-02-06 重庆邮电大学 Method suitable for broadcast authentication of wireless sensor network
CN103200563B (en) * 2013-03-28 2016-06-29 重庆邮电大学 A kind of subliminal channel anonymous communication method based on authentication code
CN104980921B (en) * 2015-06-16 2019-04-23 南京林业大学 A kind of wireless sensor network key distribution method
CN104980921A (en) * 2015-06-16 2015-10-14 南京三宝科技股份有限公司 Method for key distribution in wireless sensor network
CN105072106A (en) * 2015-07-30 2015-11-18 东南大学 Identity-based Lagrange interpolation secret key management protocol
CN105072106B (en) * 2015-07-30 2018-05-04 东南大学 A kind of Lagrange's interpolation key management method of identity-based
CN105657704A (en) * 2016-03-24 2016-06-08 北京理工大学 Integer modulus based wireless sensor network key management method
CN105657704B (en) * 2016-03-24 2019-02-15 北京理工大学 A kind of key management method of wireless sensor network based on integer modulus
CN106507347A (en) * 2017-01-09 2017-03-15 大连理工大学 A kind of key generation method for protecting wireless sensor network security
CN108833098A (en) * 2018-07-05 2018-11-16 西北大学 A kind of key management method of wireless sensor network based on Solution for System of Linear Equations
CN108833098B (en) * 2018-07-05 2021-08-03 西北大学 Wireless sensor network key management method based on linear equation block solution
CN109617691A (en) * 2018-11-19 2019-04-12 兰州大学 Group's authentication method and system of modular arithmetic is used in Multiuser certification
CN113726511A (en) * 2021-08-31 2021-11-30 南方电网科学研究院有限责任公司 Demand communication key distribution method and system based on Chinese remainder theorem
CN113726511B (en) * 2021-08-31 2024-02-06 南方电网科学研究院有限责任公司 On-demand communication key distribution method and system based on China remainder theorem
CN114339746A (en) * 2021-12-31 2022-04-12 中国科学技术大学 China remainder theorem-based dynamic group key management method and system for Internet of vehicles
CN114339746B (en) * 2021-12-31 2023-11-17 中国科学技术大学 Internet of vehicles dynamic group key management method and system based on China remainder theorem

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Application publication date: 20120704